Solve 3/2*(1/5-2/1*5/2)-0.75+frac{1}{4}=

$$\frac { 3 } { 2 } \cdot ( \frac { 1 } { 5 } - \frac { 2 } { 1 } \cdot \frac { 5 } { 2 } ) - 0.75 + \frac { 1 } { 4 } =$$

Evaluate

$$-7.7$$

Solution Steps

Anything divided by one gives itself.

$$\frac{3}{2}\left(\frac{1}{5}-2\times \frac{5}{2}\right)-0.75+\frac{1}{4}$$

Cancel out 2 and 2.

$$\frac{3}{2}\left(\frac{1}{5}-5\right)-0.75+\frac{1}{4}$$

Convert 5 to fraction \frac{25}{5}.

$$\frac{3}{2}\left(\frac{1}{5}-\frac{25}{5}\right)-0.75+\frac{1}{4}$$

Since \frac{1}{5} and \frac{25}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}\times \frac{1-25}{5}-0.75+\frac{1}{4}$$

Subtract 25 from 1 to get -24.

$$\frac{3}{2}\left(-\frac{24}{5}\right)-0.75+\frac{1}{4}$$

Multiply \frac{3}{2} times -\frac{24}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-24\right)}{2\times 5}-0.75+\frac{1}{4}$$

Do the multiplications in the fraction \frac{3\left(-24\right)}{2\times 5}.

$$\frac{-72}{10}-0.75+\frac{1}{4}$$

Reduce the fraction \frac{-72}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{36}{5}-0.75+\frac{1}{4}$$

Convert decimal number 0.75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{36}{5}-\frac{3}{4}+\frac{1}{4}$$

Least common multiple of 5 and 4 is 20. Convert -\frac{36}{5} and \frac{3}{4} to fractions with denominator 20.

$$-\frac{144}{20}-\frac{15}{20}+\frac{1}{4}$$

Since -\frac{144}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-144-15}{20}+\frac{1}{4}$$

Subtract 15 from -144 to get -159.

$$-\frac{159}{20}+\frac{1}{4}$$

Least common multiple of 20 and 4 is 20. Convert -\frac{159}{20} and \frac{1}{4} to fractions with denominator 20.

$$-\frac{159}{20}+\frac{5}{20}$$

Since -\frac{159}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{-159+5}{20}$$

Add -159 and 5 to get -154.

$$\frac{-154}{20}$$

Reduce the fraction \frac{-154}{20} to lowest terms by extracting and canceling out 2.

$$-\frac{77}{10}$$

Factor

$$-7.7$$